# Browsing by Subject "Trajectory"

Now showing 1 - 10 of 10

- Results Per Page
1 5 10 20 40 60 80 100

- Sort Options
Ascending Descending

Item A complete and fast survey of the orbital insertion design space for planetary moon missions(2017-08-10) See, Robert Harding; Russell, Ryan Paul, 1976-Show more The most expensive maneuver for an interplanetary spacecraft is the orbital injection. One approach to find minimum fuel-cost trajectories is to preform a search over a number of design parameters such as radius of periapse, apoapse of the insertion orbit, and angle of approach. The so-called V-infinity leveraging maneuver has been shown to reduce the design space by implementing a small burn at apoapse to modify the velocity vector at a flyby body. The focus of the present work is orbital insertion of a science mission at Jupiter or Saturn, with the end goal of rendezvousing with a high-science priority moon such at Titan or Europa. The orbital insertion phase is framed as a boundary-value problem with a 1-D minimization over Time-Of-Flight (TOF) and assumes two body dynamics which enables both rapid and broad trajectory searches. Specifically, a search over Body-Plane (B-Plane) Angle and TOF is presented and then, upon finding a minimum-[Delta] V B-Plane Angle, searches over radius of periapse. Additionally, analytic solutions for B-Plane Angle are derived for the special cases of minimum inclination, node/apse alignment, and moon/apse alignment.Show more Item A critical evaluation of modern low-thrust, feedback-driven spacecraft control laws(2012-12) Hatten, Noble Ariel; Ocampo, Cesar; Akella, MaruthiShow more Low-thrust spacecraft trajectory optimization is often a difficult and time-consuming process. One alternative is to instead use a closed-loop, feedback-driven control law, which calculates the control using knowledge of only the current state and target state, and does not require the solution of a nonlinear optimization problem or system of nonlinear equations. Though generally suboptimal, such control laws are attractive because of the ease and speed with which they may be implemented and used to calculate feasible low-thrust maneuvers. This thesis presents the theoretical foundations for seven modern low-thrust control laws based on control law "blending" and Lyapunov control theory for a particle spacecraft operating in an inverse-square gravitational field. The control laws are evaluated critically to determine those that present the best combinations of thoroughness of method and minimization of user input required. The three control laws judged to exhibit the most favorable characteristics are then compared quantitatively through three numerical simulations. The simulations demonstrate the effectiveness of feedback-driven control laws, but also reveal several situations in which the control laws may perform poorly or break down altogether due to either theoretical shortcomings or numerical difficulties. The causes and effects of these issues are explained, and methods of handling them are proposed, implemented, and evaluated. Various opportunities for further work in the area are also described.Show more Item Designing a laboratory model test program for developing a new offshore anchor(2015-05) Huang, Yunhan; Gilbert, Robert B. (Robert Bruce), 1965-; Rathje, Ellen MShow more The Flying Wing Anchor (patent pending) is a new anchor concept that combines the features of dynamically penetrating anchors, drag embedment anchors, and plate anchors. To study and optimize the behavior of the new anchor, this study developed a simplified predictive model and a new data acquisition system for performing physical model tests. The simplified predictive model couples a limit-equilibrium-based model for the anchor line and a plasticity-based model for the anchor to predict the embedment trajectory and holding capacity of the new anchor. The new data acquisition system is used to record data from sensors and control the movement of an electric motor. The system was developed by LabVIEW and demonstrated with a model test. The following major conclusions are drawn from this work about the behavior of this anchor concept in clay: (1) The pitch angle at the initiation of dive can be optimized to achieve the maximum dive depth and ultimate holding capacity. (2) The maximum depth of the dive is not strongly dependent on the undrained shear strength of the soil, while the ultimate holding capacity is proportional to the undrained shear strength of the soil at the maximum dive depth. (3) A smaller diameter of the line makes the anchor dive deeper and increases the ultimate capacity. (4) A deeper initial embedment depth after free fall makes the anchor dive deeper and increases the ultimate capacity. (5) A series of model tests to calibrate the simplified predictive model for the performance of the anchor should consist of varying the thickness of the line, the depth of initial embedment, the pitch angle at the initiation of dive, and the profile of undrained shear strength versus depth. It is recommended that model tests be conducted using the guidance presented in this thesis.Show more Item Initial guess and optimization strategies for multi-body space trajectories with application to free return trajectories to near-Earth asteroids(2014-08) Bradley, Nicholas Ethan; Russell, Ryan Paul, 1976-; Ocampo, CesarShow more This concept of calculating, optimizing, and utilizing a trajectory known as a ``Free Return Trajectory" to facilitate spacecraft rendezvous with Near-Earth Asteroids is presented in this dissertation. A Free Return Trajectory may be defined as a trajectory that begins and ends near the same point, relative to some central body, without performing any deterministic velocity maneuvers (i.e., no maneuvers are planned in a theoretical sense for the nominal mission to proceed). Free Return Trajectories have been utilized previously for other purposes in astrodynamics, but they have not been previously applied to the problem of Near-Earth Asteroid rendezvous. Presented here is a series of descriptions, algorithms, and results related to trajectory initial guess calculation and optimal trajectory convergence. First, Earth-centered Free Return Trajectories are described in a general manner, and these trajectories are classified into several families based on common characteristics. Next, these trajectories are used to automatically generate initial conditions in the three-body problem for the purpose of Near-Earth Asteroid rendezvous. For several bodies of interest, example initial conditions are automatically generated, and are subsequently converged, resulting in feasible, locally-optimal, round-trip trajectories to Near-Earth Asteroids utilizing Free Return Trajectories. Subsequently, a study is performed on using an unpowered flyby of the Moon to lower the overall DV cost for a nominal round-trip voyage to a Near-Earth Asteroid. Using the Moon is shown to appreciably decrease the overall mission cost. In creating the formulation and algorithms for the Lunar flyby problem, an initial guess routine for generic planetary and lunar flyby tours was developed. This continuation algorithm is presented next, and details a novel process by which ballistic trajectories in a simplistic two-body force model may be iteratively converged in progressively more realistic dynamical models until a final converged ballistic trajectory is found in a full-ephemeris, full-dynamics model. This procedure is useful for constructing interplanetary transfers and moon tours in a realistic dynamical framework; an interplanetary and an inter-moon example are both shown. To summarize, the material in this dissertation consists of: novel algorithms to compute Free Return Trajectories, and application of the concept to Near-Earth Asteroid rendezvous; demonstration of cost-savings by using a Lunar flyby; and a novel routine to transfer trajectories from a simplistic model to a more realistic dynamical representation.Show more Item Patched conic interplanetary trajectory design tool(2011-12) Brennan, Martin James; Fowler, Wallace T.; Ocampo, CesarShow more One of the most important aspects of preliminary interplanetary mission planning entails designing a trajectory that delivers a spacecraft to the required destinations and accomplishes all the objectives. The design tool described in this thesis allows an investigator to explore various interplanetary trajectories quickly and easily. The design tool employs the patched conic method to determine heliocentric and planetocentric trajectory information. An existing Lambert Targeting routine and other common algorithms are utilized in conjunction with the design tool’s specialized code to formulate an entire trajectory from Earth departure to arrival at the destination. The tool includes many options for the investigator to accurately configure the desired trajectory, including planetary gravity assists, deep space maneuvers, and various departure and arrival conditions. The trajectory design tool is coded in MATLAB, which provides access to three dimensional plotting options and user adaptability. The design tool also incorporates powerful MATLAB optimization functions that adjust trajectory characteristics to find a configuration that yields the minimum spacecraft propellant in the form of change in velocity.Show more Item Preliminary design of spacecraft trajectories for missions to outer planets and small bodies(2015-08) Lantukh, Demyan Vasilyevich; Russell, Ryan Paul, 1976-; Fowler, Wallace; Bettadpur, Srinivas; Guo, Yanping; Broschart, StephenShow more Multiple gravity assist (MGA) spacecraft trajectories can be difficult to find, an intractable problem to solve completely. However, these trajectories have enormous benefits for missions to challenging destinations such as outer planets and primitive bodies. Techniques are presented to aid in solving this problem with a global search tool and additional investigation into one particular proximity operations option is discussed. Explore is a global grid-search MGA trajectory pathsolving tool. An efficient sequential tree search eliminates v∞ discontinuities and prunes trajectories. Performance indices may be applied to further prune the search, with multiple objectives handled by allowing these indices to change between trajectory segments and by pruning with a Pareto-optimality ranking. The MGA search is extended to include deep space maneuvers (DSM), v∞ leveraging transfers (VILT) and low-thrust (LT) transfers. In addition, rendezvous or nπ sequences can patch the transfers together, enabling automatic augmentation of the MGA sequence. Details of VILT segments and nπ sequences are presented: A boundaryvalue problem (BVP) VILT formulation using a one-dimensional root-solve enables inclusion of an efficient class of maneuvers with runtime comparable to solving ballistic transfers. Importantly, the BVP VILT also allows the calculation of velocity-aligned apsidal maneuvers (VAM), including inter-body transfers and orbit insertion maneuvers. A method for automated inclusion of nπ transfers such as resonant returns and back-flip trajectories is introduced: a BVP is posed on the v∞ sphere and solved with one or more nπ transfers – which may additionally fulfill specified science objectives. The nπ sequence BVP is implemented within the broader search, combining nπ and other transfers in the same trajectory. To aid proximity operations around small bodies, analytical methods are used to investigate stability regions in the presence of significant solar radiation pressure (SRP) and body oblateness perturbations. The interactions of these perturbations allow for heliotropic orbits, a stable family of low-altitude orbits investigated in detail. A novel constrained double-averaging technique analytically determines inclined heliotropic orbits. This type of knowledge is uniquely valuable for small body missions where SRP and irregular body shape are very important and where target selection is often a part of the mission design.Show more Item Preliminary interplanetary trajectory design tools using ballistic and powered gravity assists(2015-08) Brennan, Martin James; Fowler, Wallace T.; Russell, Ryan; Bettadpur, Srinivas; Lightsey, E G; Olsen, CarrieShow more Preliminary interplanetary trajectory designs frequently use simplified two-body orbital mechanics and linked conics methodology to model the complex trajectories in multi-body systems. Incorporating gravity assists provides highly efficient interplanetary trajectories, enabling otherwise infeasible spacecraft missions. Future missions may employ powered gravity assists, using a propulsive maneuver during the flyby, improving the overall trajectory performance. This dissertation provides a complete description and analysis of a new interplanetary trajectory design tool known as TRACT (TRAjectory Configuration Tool). TRACT is capable of modeling complex interplanetary trajectories, including multiple ballistic and/or powered gravity assists, deep space maneuvers, parking orbits, and other common maneuvers. TRACT utilizes an adaptable architecture of modular boundary value problem (BVP) algorithms for all trajectory segments. A bi-level optimization scheme is employed to reduce the number of optimization variables, simplifying the user provided trajectory information. The standardized optimization parameter set allows for easy use of TRACT with a variety of optimization algorithms and mission constraints. The dissertation also details new research in powered gravity assists. A review of literature on optimal powered gravity assists is presented, where many optimal solutions found are infeasible for realistic spacecraft missions. The need was identified for a mission feasible optimal powered gravity assist algorithm using only a single impulsive maneuver. The solution space was analyzed and a complete characterization was developed for solution types of the optimal single-impulse powered gravity assist. Using newfound solution space characteristics, an efficient and reliable optimal single-impulse powered gravity assist BVP algorithm was formulated. The mission constraints were strictly enforced, such as maintaining the closest approach above a minimum radius and below a maximum radius. An extension of the optimal powered gravity assist research is the development of a gravity assist BVP algorithm that utilizes an asymptote ΔV correction maneuver to produce ballistic gravity assist trajectory solutions. The efficient algorithm is tested with real interplanetary mission trajectory parameters and successfully converges upon ballistic gravity assists with improved performance compared to traditional methods. A hybrid approach is also presented, using the asymptote maneuver algorithm together with traditional gravity assist constraints to reach ballistic trajectory solutions more reliably, while improving computational performance.Show more Item Space object translational and rotational state prediction and sensitivity calculation(2016-12) Hatten, Noble Ariel; Russell, Ryan Paul, 1976-; Akella, Maruthi R; Bettadpur, Srinivas V; Jones, Brandon A; Weisman, Ryan MShow more While computing power has grown monumentally during the space age, the demands of astrodynamics applications have more than kept pace. Resources are taxed by the ever-growing number of Earth-orbiting space objects (SOs) that must be tracked to maintain space situational awareness (SSA) and by increasingly popular but computationally expensive tools like Monte Carlo techniques and stochastic optimization algorithms. In this dissertation, methods are presented to improve the accuracy, efficiency, and utility of SO state prediction and sensitivity calculation algorithms. The dynamical model of the low Earth orbit regime is addressed through the introduction of an upgraded Harris-Priester atmospheric density model, which introduces a smooth polynomial dependency on solar flux. Additional modifications eliminate singularities and provide smooth partial derivatives of the density with respect to SO state, time, and solar conditions. The numerical solution of the equations of motion derived from dynamics models is also addressed, with particular emphasis placed on six-degree-of-freedom (6DOF) state prediction. Implicit Runge-Kutta (IRK) methods are applied to the 6DOF problem, and customizations, including variable-fidelity dynamics models and parallelization, are introduced to maximize efficiency and take advantage of modern computing architectures. Sensitivity calculation -- a necessity for SSA and other applications -- via RK methods is also examined. Linear algebraic systems for first- and second-order state transition matrix calculation are derived by directly differentiating either the first- or second-order form of the RK update equations. This approach significantly reduces the required number of Jacobian and Hessian evaluations compared to the ubiquitous augmented state vector approach for IRK methods, which can result in more efficient calculations. Parallelization is once again leveraged to reduce the runtime of IRK methods. Finally, a hybrid special perturbation/general perturbation (SP/GP) technique is introduced to address the notoriously slow speed of fully coupled 6DOF state prediction. The hybrid method uses a GP rotational state prediction to provide low-fidelity attitude information for a high-fidelity 3DOF SP routine. This strategy allows for the calculation of body forces using arbitrary shape models without adding attitude to the propagated state or taking the small step sizes often required by full 6DOF propagation. The attitude approximation is obtained from a Lie-Deprit perturbation result previously applied to SOs in circular orbits subject to gravity-gradient torque and extended here to SOs in elliptical orbits. The hybrid method is shown to produce a meaningful middle ground between 3DOF SP and 6DOF SP methods in the accuracy vs. efficiency space.Show more Item Spacecraft trajectory optimization using many embedded Lambert problems(2022-08-10) Ottesen, David Ryan; Russell, Ryan Paul, 1976-; Akella, Maruthi R; Jones, Brandon A; Fridovich-Keil, David; Guo, YanpingShow more Improvement of spacecraft trajectory optimization approaches, methods, and techniques is critical for better mission design. Preliminary low-fidelity analysis precedes high-fidelity analysis to efficiently explore the space of a problem. The work of this dissertation extends an embedded boundary value problem (EBVP) technique for preliminary design in the two-body problem. The EBVP technique is designed for direct, unconstrained optimization using many, short-arc, embedded Lambert problems that discretize the trajectory. The short arcs share terminal positions to implicitly enforce position continuity and the instantaneous velocity discontinuities in between segments are the control. These coasting arcs and impulsive maneuvers in between segments are defined collectively as a coast-impulse model, similar to the well-known Sims-Flanagan model. Use of EBVPs is not new to spacecraft trajectory optimization, extensively used in primer vector theory, flyby-tour design, direct impulsive-maneuver optimization, and more. Lack of fast and accurate BVP solvers has prevented the use of the EBVP technique on problems with more than dozens of segments. For the two-body problem, a recently-developed Lambert solver, complete with the necessary partials, enables the extension of the EBVP technique to many hundreds to thousands of segments and hundreds of revolutions. The use of many short arcs guarantees existence and uniqueness for the Lambert problem of each segment. Furthermore, short arcs simultaneously approximate low thrust and eliminates the need to know the structure of a high-thrust impulsive-maneuver solution. A set of examples show the EBVP technique to be efficient, robust, and useful. In particular, an example using 256 revolutions, 6143 segments, and a constant flight time per segment, optimizes in 5.5 hours using a single processor. After this initial demonstration, the EBVP technique is improved by a function which enables variable flight time per segment. Guided by the well-known Sundman transformation, these piecewise Sundman transformation (PST) functions divide the total flight time of the trajectory into spatially-even arcs, importantly not modifying the dynamics. Flight-time functions and their dynamical regularization counterpart are shown to share similar behavior for Keplerian orbit propagation. The PST functions are also shown to extend the EBVP technique to a large design space, where a runtime-feasible transfer with 512 revs and 12287 segments is presented that significantly changes semimajor axis, eccentricity, and inclination. Moreover, another example is presented that transfers through the numerically challenging parabolic boundary, i.e. a transfer from a circular to hyperbolic orbit. Both these examples use an exponent of 3/2 for the PST to enforce the spatially-even arcs or equal steps in eccentric anomaly. Lastly, an optimal control problem is formulated to solve a class of many-revolution trajectories relevant to the EBVP technique. For transfers that minimize thrust-acceleration-squared, primer vector theory enables the mapping of direct, many-impulsive-maneuver trajectories to the indirect, continuous-thrust-acceleration equivalent. The mapping algorithm is independent of how the direct solution is obtained and the mapping computations only require a solver for a BVP and its partial derivatives. For the two-body problem, a Lambert solver is used. The mapping is simple because the impulsive maneuvers and co-states share the same linear space around an optimal trajectory. For numerical results, the direct coast-impulse solutions are demonstrated to converge to the indirect continuous solutions as the number of impulses and segments increase. The two-body design space is explored with a set of three many-revolution, many-segment examples changing semimajor axis, eccentricity, and inclination. The first two examples change either a small amount of semimajor axis or eccentricity, and the third example is a transfer to geosynchronous orbit. Using a single processor, the optimization runtime is seconds to minutes for revolution counts of 10 to 100, while on the order of one hour for examples with up to 500 revolutions. Any of these thrust-acceleration-squared solutions are good candidates to start a homotopy to a higher-fidelity minimization problem with practical constraints.Show more Item Turbulent jet breakup : theory and data(2020-08-14) Trettel, Benjamin M.; Ezekoye, Ofodike A.; Goldstein, David B; Hall, Matthew J.; Ling, Stanley; Moser, Robert D.Show more Understanding the breakup of turbulent liquid jets is important for many applications including spray combustion, fire suppression, and water jet cutting. Turbulent jet breakup models are rarely fully predictive, and typically require re-calibration to experimental data for different cases. In this work the existing models for turbulent jet breakup are reviewed, highlighting the successes and shortcomings of existing and new approaches. A critical shortcoming of most existing models is the neglect of a measure of the strength of the turbulence like the turbulence intensity. New models are developed to address this shortcoming and others. Existing and new models are compared against a large experimental compilation, primarily from the archival literature. Because the physical mechanisms causing breakup can vary, a new regime diagram was developed in this work, allowing the breakup regime and consequently how to model a particular jet to be determined. Problems common in the validation of turbulent jet breakup models are detailed. A model for the turbulence intensity at the outlet of a nozzle is developed. Finally, a theoretical model is developed and validated for the range of a large firefighting water jet including the effects of jet breakup and air entrainmentShow more